Adoption as a social marker: Innovation diffusion with outgroup aversion

Social identities are among the key factors driving behavior in complex societies. Signals of social identity are known to influence individual behaviors in the adoption of innovations. Yet the population-level consequences of identity signaling on the diffusion of innovations are largely unknown. Here we use both analytical and agent-based modeling to consider the spread of a beneficial innovation in a structured population in which there exist two groups who are averse to being mistaken for each other. We investigate the dynamics of adoption and consider the role of structural factors such as demographic skew and communication scale on population-level outcomes. We find that outgroup aversion can lead to adoption being delayed or suppressed in one group, and that population-wide underadoption is common. Comparing the two models, we find that differential adoption can arise due to structural constraints on information flow even in the absence of intrinsic between-group differences in adoption rates. Further, we find that patterns of polarization in adoption at both local and global scales depend on the details of demographic organization and the scale of communication. This research has particular relevance to widely beneficial but identity-relevant products and behaviors, such as green technologies, where overall levels of adoption determine the positive benefits that accrue to society at large.     

Modeling Reputational and Informational Influences in Threshold Models of Bandwagon Innovation Diffusion

Bandwagon innovation diffusion is characterized by a positive feedback loop where adoptions by some actors increase the pressure to adopt for other actors. In particular, when gains from an innovation are difficult to quantify, such as implementing quality circles or downsizing practices, diffusion is likely to occur through a bandwagon process. In this paper we extend Abrahamson and Rosenkopf&2018;s (1993) model of bandwagon diffusion to examine both reputational and informational influences on this process. We find that the distribution of reputations among the set of potential adopters affects the extent of bandwagon diffusion under conditions of moderate ambiguity, and we find that bandwagons occur even when potential adopters receive information about others&2018; unprofitable experiences with the innovation.     

Agent-behaviour and network influence on energy innovation diffusion

An agent-based model is developed for investigating the role of individual behaviour and network influence on energy innovation diffusion. Behaviour is based on how agents value specific attributes of a technology, and network effects are disaggregated into indirect influence through exposure to a larger population, and direct influence through personal contacts. We find that network influence can have a positive effect on accelerating the diffusion of new energy innovations, but can be counteracted by risk adverse behaviour. Combined direct and indirect network effects can have as strong an influence on adoption behaviour as personal preferences. Interestingly, we find that indirect influence from the larger population can have a greater effect than direct personal contacts on an individual. This implies a feedback between population and sub-population level signals on adoption behaviour which warrants further exploration as a mechanism to induce individual level change.     

New product launch decisions with robust optimization

We consider a problem where a company must decide the order in which to launch new products within a given time horizon and budget constraints, and where the parameters of the adoption rate of these new products are subject to uncertainty. This uncertainty can bring significant change to the optimal launch sequence. We present a robust optimization approach that incorporates such uncertainty on the Bass diffusion model for new products as well as on the price response function of partners that collaborate with the company in order to bring its products to market. The decision-maker optimizes his worst-case profit over an uncertainty set where nature chooses the time periods in which (integer) units of the budgets of uncertainty are used for worst impact. This leads to uncertainty sets with binary variables. We show that a conservative approximation of the robust problem can nonetheless be reformulated as a mixed integer linear programming problem, is therefore of the same structure as the deterministic problem and can be solved in a tractable manner. Finally, we illustrate our approach on numerical experiments. Our model also incorporates contracts with potential commercialization partners. The key output of our work is a sequence of product launch times that protects the decision-maker against parameter uncertainty for the adoption rates of the new products and the response of potential partners to partnership offers.     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

Spatiotemporal patterns induced by delay and cross-fractional diffusion in a predator-prey model describing intraguild predation

In this article, we study a reaction-diffusion predator-prey model that describes intraguild predation. We mainly consider the effects of time delay and cross-fractional diffusion on dynamical behavior. By using delay as the bifurcation parameter, we perform a detailed Hopf bifurcation analysis and derive the algorithm for determining the direction and stability of the bifurcating periodic solutions. We also demonstrate that proper cross-fractional diffusion can induce Turing pattern, and the smaller the order of fractional diffusion is, the more easily Turing pattern is able to occur.     

网络结构、采纳者偏好与创新扩散:基于采纳者决策过程的创新扩散系统动力学模型仿真分析

在对采纳者决策过程分析的基础上,将网络结构和采纳者偏好作为核心参数,构建基于采纳者决策过程的创新扩散系统动力学模型。对模型进行仿真发现,在采纳者趋同化偏好条件下,网络平均度、网络重连概率与采纳者偏好强度的变动趋势与创新扩散效率的变动趋势相同,而在采纳者差异化偏好条件下则与创新扩散效率变动趋势相反。网络平均路径长度对创新扩散的影响方向与采纳者偏好特征无关,提高网络平均路径长度会始终降低创新扩散的效率。采纳者的趋同化偏好能够放大创新扩散对网络结构变量与采纳者偏好强度变量的敏感程度,采纳者差异化偏好则会缩小创新扩散对网络结构变量与采纳者偏好强度变量的敏感程度。研究结果对于制定创新推广策略具有一定的指导意义。     

How Do the Spatial Structure and Time Delay Affect the Persistence of A Polluted Species

In this article, we consider the effects of diffusion and time delay on the species in a polluted environment. Persistence-extinction thresholds are given for population in the toxicant stressed logistic growth model with discrete diffusion or time delay. It is proved that dispersal allows a larger threshold, that is, dispersal can increase the endurance effectiveness of the population subjected to toxicant, and time delay has no effect on the threshold result.     

THE DIFFUSION OF RESOURCE-QUALITY-AUGMENTING TECHNOLOGIES: OUTPUT SUPPLY AND INPUT DEMAND EFFECTS

This paper develops a model that shows that the adoption of a modern conservation technology is a gradual process in which dynamic patterns are determined by variation in resource quality among producers, improvements in equipment, and learning. The dynamics of technological changes are reflected in the cyclical patterns of production and resource use. A numerical example simulates adoption rates of modern irrigation technologies using California data and shows that rate of adoption is an S-shaped function of time and that water use and output are cyclical.     

Resource enablement modeling: Implications for studying the diffusion of technology

Organizations contemplating standardized technology adoption are confronted both by the potential for internal capability gains and by inter-organizational forces. Although such technologies may appear imitable and non-strategic, they can enable idiosyncrasies and strategic gains through their interaction with other resources possessed by firms. Based on Barney’s original 1991 thesis on the resource-based view, Abrahamson and Rosenkopf’s 1997 analytical framework is reconceptualized and extended to capture both internal and external elements of assessment and IT value generation. An analytical experiment is conducted on the extended model to illustrate how technology diffusion is simply one artifact of a general cycle of resource enablement that can be viewed as driving idiosyncratic strategic gains and facilitating inter-organizational dynamics.     

多元技术创新扩散的系统动力学模型及仿真

本文力图放宽模型的假设,考虑创新技术市场间的非独立性、扩散过程中潜在采用-等待采用-已采用三阶段中时间延迟性,建立多元技术创新扩散的系统动力学模型,并用Vensim进行模拟仿真研究.仿真结果表明该模型比较符合实际,可为多元技术创新扩散的理论研究和实际实施提供理论指导.     

Optimal Investment in Heterogeneous Capital and Technology Under Restricted Natural Resource

We consider the optimal control of nonlinear integral equations with endogenous delay and state constraints, which describe a developing economy subjected to resource constraints. The economy invests in new resource-efficient technologies, invests in new capital, and scraps obsolete capital. We derive the optimality condition and determine long-term asymptotically exponential trajectories that optimally combine scrapping the dirtiest capital and developing new clean technologies. Next, we study the short-term dynamics of the model and show that it leads to a sustainable growth with active resource constraint.     

Stability analysis of the Kaldor model with time delays: monetary policy and government budget constraint

We analyze the model with monetary policy based on the Kaldor's business cycle theory. We introduce the government sector, which conducts the fiscal policy and monetary policy to stabilize the economy. The execution of such a policy needs legislation, and generally, the legislative process is time consuming. We investigate in this paper how the fiscal policy with a time delay affects stability of the economy.We assume that the monetary policy is conducted as a countermeasure of the fiscal deficit by the government, and we consider two extreme cases, namely money finance and bond finance case. In each case, when no time delay exists for the fiscal policy, Keynesian fiscal policy is the preferred method for preventing the economic fluctuations. However, it is not so simple when the time delay exists in the fiscal policy. There exists the policy, which stabilizes the economy under any time delay in the money finance case. On the other hand, in the bond finance case, such a policy does not exist and as the time delay increases the economy becomes unstable. However in both cases, contrary to the expectations of the government, the stronger the fiscal policy, the more unstable the economy becomes for the short time delay.     

Traveling wavefronts in temporally discrete reaction–diffusion equations with delay

This paper is concerned with the existence of traveling wavefronts of a temporally discrete reaction–diffusion equation with delay. By using monotone iteration and upper–lower solution technique, the existence of traveling wavefronts for the temporally discrete reaction–diffusion equation with delay is established. As an application, we consider an abstract diffusive equation, which includes a single species diffusive model as a particular case. Our result implies the temporally discrete model is a good approximation of corresponding continuous time model in sense of propagation.     

Price subsidies and guaranteed buys of a new technology

We consider a problem of a government that wishes to stimulate the adoption of a new technology in order to replace an older, environmentally less desirable, technology. The new technology is manufactured by a monopolist firm which has learning-by-doing in its production process. The firm sells the new product to both private households and government institutions and wishes to determine an optimal pricing policy. The government has at its disposal two instruments: subsidizing the consumer price and making purchases of the new technology from the firm. We assume profit maximization on the part of the firm. The government wishes to maximize the cumulative number of units of the new technology sold to private households by the terminal date of the government program. The problem is set up as a Stackelberg differential game in which we identify an open-loop equilibrium, supposing that the government can credibly precommit to its subsidy and buying program.     

Truncating the hierarchy of moment equations based on point distribution—application to innovation diffusion

The phenomenon of innovation diffusion, modeled as a nonlinear birth process, leads to a hierarchy of moment equations. For gaining insight into the evolution of moments of a number of adopters in innovation diffusion, truncation procedures based on point distributions are proposed for truncating the hierarchy of moment equations. It is found that the results obtained by employing new truncation procedures are in close agreement with analytical results based on system size expansion for large population size.     

Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model

Infection with HIV-1, degrading the human immune system and recent advances of drug therapy to arrest HIV-1 infection, has generated considerable research interest in the area. Bonhoeffer et al. (1997) [1], introduced a population model representing long term dynamics of HIV infection in response to available drug therapies. We consider a similar type of approximate model incorporating time delay in the process of infection on the healthy T cells which, in turn, implies inclusion of a similar delay in the process of viral replication. The model is studied both analytically and numerically. We also include a similar delay in the killing rate of infected CD4⁺ T cells by Cytotoxic T-Lymphocyte (CTL) and in the stimulation of CTL and analyse two resulting models numerically.The models with no time delay present have two equilibria: one where there is no infection and a non-trivial equilibrium where the infection can persist. If there is no time delay then the non-trivial equilibrium is locally asymptotically stable. Both our analytical results (for the first model) and our numerical results (for all three models) indicate that introduction of a time delay can destabilize the non-trivial equilibrium. The numerical results indicate that such destabilization occurs at realistic time delays and that there is a threshold time delay beneath which the equilibrium with infection present is locally asymptotically stable and above which this equilibrium is unstable and exhibits oscillatory solutions of increasing amplitude.     

Cognitive modeling of socially transmitted affordances: a computational model of behavioral adoption tested against archival data from the Stanford Prison Experiment

Social learning and adoption of new affordances govern the rise of new a variety of behaviors, from actions as mundane as dance steps to those as dangerous as new ways to make improvised explosive device (IED) detonators. Traditional diffusion models and social network structures fail to adequately explain who would be likely to imitate new behavior and why some agents adopt the behavior while others do not. To address this gap, a cognitive model was designed that represents well-known socio-cognitive factors of attention, social influence, and motivation that influence learning and adoption of new behavior. This model was implemented in the Performance Moderator Function Server (PMFServ) agent-based cognitive architecture, enabling the creation of simulations where affordances spread memetically through cognitive mechanisms. This approach models facets of behavioral adoption that have not been explored by existing architectures: unintentional learning, multi-layered social and environmental attention cues, and contextual adoption. To examine the effectiveness of this model, its performance was tested against data from the Stanford Prison Experiment collected from the Archives of the History of American Psychology.     

Fitted Galerkin spectral method to solve delay partial differential equations

In this paper, we consider a class of parabolic partial differential equations with a time delay. The first model equation is the mixed problems for scalar generalized diffusion equation with a delay, whereas the second model equation is a delayed reaction‐diffusion equation. Both of these models have inherent complex nature because of which their analytical solutions are hardly obtainable, and therefore, one has to seek numerical treatments for their approximate solutions. To this end, we develop a fitted Galerkin spectral method for solving this problem. We derive optimal error estimates based on weak formulations for the fully discrete problems. Some numerical experiments are also provided at the end. Copyright © 2015 John Wiley & Sons, Ltd.     

Solving a final value fractional diffusion problem by boundary condition regularization

The evolution process of fractional order describes some phenomenon of anomalous diffusion and transport dynamics in complex system. The equation containing fractional derivatives provides a suitable mathematical model for describing such a process. The initial boundary value problem is hard to solve due to the nonlocal property of the fractional order derivative. We consider a final value problem in a bounded domain for fractional evolution process with respect to time, which means to recover the initial state for some slow diffusion process from its present status. For this ill-posed problem, we construct a regularizing solution using quasi-reversible method. The well-posedness of the regularizing solution as well as the convergence property is rigorously analyzed. The advantage of the proposed scheme is that the regularizing solution is of the explicit analytic solution and therefore is easy to be implemented. Numerical examples are presented to show the validity of the proposed scheme.